Math CentralQuandaries & Queries


Question from Jim:

What is the meaning of the phrase ‘one part in 10x” where the x is an exponent? I have seen these examples: “...better than one part in 10x” and “ within one part in 10x.”

Hi Jim,

$10^x$ where $x$ is a positive integer is the number obtained by multiplying 10 by itself $x$ times. If you can't type exponents $10^x$ is often written 10^x. Hence for example

$10^2 = 10 \times 10 = 100$
$10^3 = 10 \times 10 \times 10 = 1,000$
and $10^9 = 1,000,000,000$ which is one billion.

Hence better than one part in $10^9$ is better than one part in a billion.

Write back if this is not what you needed,

Jim wrote back

Penny Nom, I understand how an exponent works. 10^2 = 100. I am wondering about the phrase "one part in." For example, what is meant by "better than one part in 100"? And what is meant by "to within one part in 100"?

Hi again Jim,

Sorry I misinterpreted your question. I have been looking for an example. I looked on the internet and found a site which claims to give the diamond to ore ratio in diamond mines. Their claim is that there is approximately 1 carat of diamond in 7.35 tons of ore. 1 carat is 0.2 grams and 7.35 tons is 6,667.81 kilograms (I asked Google). Hence there is approximately $5 \times 0.2 = 1$ gram of diamond in $5 \times 6,667.81 = 33,339,050$ grams of ore. That's approximately 1 gram in $3.3 \times 10^8$ grams of ore.

Finally if I was trying to convince you to buy stock in a diamond mine I might have success if I can say "My mine's yield in weight of diamond in its ore is better than 1 part in $3.0 \times 10^{8}.$"

I hope this helps,

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